The Extended Exponentially Weighted Moving Average(extended EWMA)control chart is one of the control charts and can be used to quickly detect a small shift.The performance of control charts can be evaluated with the a...The Extended Exponentially Weighted Moving Average(extended EWMA)control chart is one of the control charts and can be used to quickly detect a small shift.The performance of control charts can be evaluated with the average run length(ARL).Due to the deriving explicit formulas for the ARL on a two-sided extended EWMA control chart for trend autoregressive or trend AR(p)model has not been reported previously.The aim of this study is to derive the explicit formulas for the ARL on a two-sided extended EWMA con-trol chart for the trend AR(p)model as well as the trend AR(1)and trend AR(2)models with exponential white noise.The analytical solution accuracy was obtained with the extended EWMA control chart and was compared to the numer-ical integral equation(NIE)method.The results show that the ARL obtained by the explicit formula and the NIE method is hardly different,but the explicit for-mula can help decrease the computational(CPU)time.Furthermore,this is also expanded to comparative performance with the Exponentially Weighted Moving Average(EWMA)control chart.The performance of the extended EWMA control chart is better than the EWMA control chart for all situations,both the trend AR(1)and trend AR(2)models.Finally,the analytical solution of ARL is applied to real-world data in the healthfield,such as COVID-19 data in the United Kingdom and Sweden,to demonstrate the efficacy of the proposed method.展开更多
This study presents an innovative development of the exponentially weighted moving average(EWMA)control chart,explicitly adapted for the examination of time series data distinguished by seasonal autoregressive moving ...This study presents an innovative development of the exponentially weighted moving average(EWMA)control chart,explicitly adapted for the examination of time series data distinguished by seasonal autoregressive moving average behavior—SARMA(1,1)L under exponential white noise.Unlike previous works that rely on simplified models such as AR(1)or assume independence,this research derives for the first time an exact two-sided Average Run Length(ARL)formula for theModified EWMAchart under SARMA(1,1)L conditions,using a mathematically rigorous Fredholm integral approach.The derived formulas are validated against numerical integral equation(NIE)solutions,showing strong agreement and significantly reduced computational burden.Additionally,a performance comparison index(PCI)is introduced to assess the chart’s detection capability.Results demonstrate that the proposed method exhibits superior sensitivity to mean shifts in autocorrelated environments,outperforming existing approaches.The findings offer a new,efficient framework for real-time quality control in complex seasonal processes,with potential applications in environmental monitoring and intelligent manufacturing systems.展开更多
This study aims to examine the explicit solution for calculating the Average Run Length(ARL)on the triple exponentially weighted moving average(TEWMA)control chart applied to autoregressive model(AR(p)),where AR(p)is ...This study aims to examine the explicit solution for calculating the Average Run Length(ARL)on the triple exponentially weighted moving average(TEWMA)control chart applied to autoregressive model(AR(p)),where AR(p)is an autoregressive model of order p,representing a time series with dependencies on its p previous values.Additionally,the study evaluates the accuracy of both explicit and numerical integral equation(NIE)solutions for AR(p)using the TEWMA control chart,focusing on the absolute percentage relative error.The results indicate that the explicit and approximate solutions are in close agreement.Furthermore,the study investigates the performance of exponentially weighted moving average(EWMA)and TEWMA control charts in detecting changes in the process,using the relative mean index(RMI)as a measure.The findings demonstrate that the TEWMA control chart outperforms the EWMA control chart in detecting process changes,especially when the value ofλis sufficiently large.In addition,an analysis using historical data from the SET index between January 2024 and May 2024 and historical data of global annual plastic production,the results of both data sets also emphasize the superior performance of the TEWMA control chart.展开更多
针对两个正态随机变量比率(Ratio of Two Normal Random Variables,RZ)监控的研究是近年来统计过程控制的重要方向之一。为了进一步提高传统休哈特型RZ控制图对过程中较小或中等参数偏移的灵敏度,本文以指数加权移动平均(Exponentially ...针对两个正态随机变量比率(Ratio of Two Normal Random Variables,RZ)监控的研究是近年来统计过程控制的重要方向之一。为了进一步提高传统休哈特型RZ控制图对过程中较小或中等参数偏移的灵敏度,本文以指数加权移动平均(Exponentially Weighted Moving Average,EWMA) RZ控制图为基础,提出了一种新的RZ控制图。首先,对EWMA-RZ控制图的平滑系数进行两次加权,提出了二次指数加权移动平均(Double EWMA,DEWMA) RZ控制图,并进一步引入了变采样间隔(Variable Sampling Interval,VSI)特性,提出了VSI-DEWMA-RZ控制图;其次,采用蒙特卡罗(Monte-Carlo,MC)仿真模拟所提出控制图的运行链长分布特征,并详细分析了控制图的性能;再次,针对不同的控制图参数,比较了VSI-DEWMA-RZ控制图与DEWMA-RZ和VSI-EWMA-RZ控制图的性能。仿真结果表明,本文提出的VSI-DEWMA-RZ控制图优于DEWMA-RZ控制图,且其对过程中较小和中等偏移的监控效果优于现有的VSI-EWMA-RZ控制图。最后,通过监控食品加工过程中“南瓜籽”和“亚麻籽”的重量,进一步说明了所提出控制图的优越性。展开更多
Objective:To define the alert levels for the total number of COVID-19 cases derived by using quantile functions to monitor COVID-19 outbreaks via an exponentially weighted moving-average(EWMA)control chart based on th...Objective:To define the alert levels for the total number of COVID-19 cases derived by using quantile functions to monitor COVID-19 outbreaks via an exponentially weighted moving-average(EWMA)control chart based on the first hitting time of the total number of COVID-19 cases following a symmetric logistic growth curve.Methods:The cumulative distribution function of the time for the total number of COVID-19 cases was used to construct a quantile function for classifying COVID-19 alert levels.The EWMA control chart control limits for monitoring a COVID-19 outbreak were formulated by applying the delta method and the sample mean and variance method.Samples were selected from countries and region including Thailand,Singapore,Vietnam,and Hong Kong to generate the total number of COVID-19 cases from February 15,2020 to December 16,2020,all of which followed symmetric patterns.A comparison of the two methods was made by applying them to a EWMA control chart based on the first hitting time for monitoring the COVID-19 outbreak in the sampled countries and region.Results:The optimal first hitting times for the EWMA control chart for monitoring COVID-19 outbreaks in Thailand,Singapore,Vietnam,and Hong Kong were approximately 280,208,286,and 298 days,respectively.Conclusions:The findings show that the sample mean and variance method can detect the first hitting time better than the delta method.Moreover,the COVID-19 alert levels can be defined into four stages for monitoring COVID-19 situation,which help the authorities to enact policies that monitor,control,and protect the population from a COVID-19 outbreak.展开更多
利用Burr分布来近似各种非正态分布对非正态情形下的EWM A均值控制图进行可变抽样区间设计,采用M arkov cha in方法计算过程的平均报警时间,数据结果显示,所设计的控制图较常规的固定抽样区间控制图可能够缩短过程失控时间从而提高控制...利用Burr分布来近似各种非正态分布对非正态情形下的EWM A均值控制图进行可变抽样区间设计,采用M arkov cha in方法计算过程的平均报警时间,数据结果显示,所设计的控制图较常规的固定抽样区间控制图可能够缩短过程失控时间从而提高控制图的效率。展开更多
基金Thailand Science ResearchInnovation Fund,and King Mongkut's University of Technology North Bangkok Contract No.KMUTNB-FF-65-45.
文摘The Extended Exponentially Weighted Moving Average(extended EWMA)control chart is one of the control charts and can be used to quickly detect a small shift.The performance of control charts can be evaluated with the average run length(ARL).Due to the deriving explicit formulas for the ARL on a two-sided extended EWMA control chart for trend autoregressive or trend AR(p)model has not been reported previously.The aim of this study is to derive the explicit formulas for the ARL on a two-sided extended EWMA con-trol chart for the trend AR(p)model as well as the trend AR(1)and trend AR(2)models with exponential white noise.The analytical solution accuracy was obtained with the extended EWMA control chart and was compared to the numer-ical integral equation(NIE)method.The results show that the ARL obtained by the explicit formula and the NIE method is hardly different,but the explicit for-mula can help decrease the computational(CPU)time.Furthermore,this is also expanded to comparative performance with the Exponentially Weighted Moving Average(EWMA)control chart.The performance of the extended EWMA control chart is better than the EWMA control chart for all situations,both the trend AR(1)and trend AR(2)models.Finally,the analytical solution of ARL is applied to real-world data in the healthfield,such as COVID-19 data in the United Kingdom and Sweden,to demonstrate the efficacy of the proposed method.
基金financially by the National Research Council of Thailand(NRCT)under Contract No.N42A670894.
文摘This study presents an innovative development of the exponentially weighted moving average(EWMA)control chart,explicitly adapted for the examination of time series data distinguished by seasonal autoregressive moving average behavior—SARMA(1,1)L under exponential white noise.Unlike previous works that rely on simplified models such as AR(1)or assume independence,this research derives for the first time an exact two-sided Average Run Length(ARL)formula for theModified EWMAchart under SARMA(1,1)L conditions,using a mathematically rigorous Fredholm integral approach.The derived formulas are validated against numerical integral equation(NIE)solutions,showing strong agreement and significantly reduced computational burden.Additionally,a performance comparison index(PCI)is introduced to assess the chart’s detection capability.Results demonstrate that the proposed method exhibits superior sensitivity to mean shifts in autocorrelated environments,outperforming existing approaches.The findings offer a new,efficient framework for real-time quality control in complex seasonal processes,with potential applications in environmental monitoring and intelligent manufacturing systems.
基金the National Science,Research and Innovation Fund(NSRF)King Mongkuts University of Technology North Bangkok under contract no.KMUTNB-FF-68-B-08.
文摘This study aims to examine the explicit solution for calculating the Average Run Length(ARL)on the triple exponentially weighted moving average(TEWMA)control chart applied to autoregressive model(AR(p)),where AR(p)is an autoregressive model of order p,representing a time series with dependencies on its p previous values.Additionally,the study evaluates the accuracy of both explicit and numerical integral equation(NIE)solutions for AR(p)using the TEWMA control chart,focusing on the absolute percentage relative error.The results indicate that the explicit and approximate solutions are in close agreement.Furthermore,the study investigates the performance of exponentially weighted moving average(EWMA)and TEWMA control charts in detecting changes in the process,using the relative mean index(RMI)as a measure.The findings demonstrate that the TEWMA control chart outperforms the EWMA control chart in detecting process changes,especially when the value ofλis sufficiently large.In addition,an analysis using historical data from the SET index between January 2024 and May 2024 and historical data of global annual plastic production,the results of both data sets also emphasize the superior performance of the TEWMA control chart.
文摘针对两个正态随机变量比率(Ratio of Two Normal Random Variables,RZ)监控的研究是近年来统计过程控制的重要方向之一。为了进一步提高传统休哈特型RZ控制图对过程中较小或中等参数偏移的灵敏度,本文以指数加权移动平均(Exponentially Weighted Moving Average,EWMA) RZ控制图为基础,提出了一种新的RZ控制图。首先,对EWMA-RZ控制图的平滑系数进行两次加权,提出了二次指数加权移动平均(Double EWMA,DEWMA) RZ控制图,并进一步引入了变采样间隔(Variable Sampling Interval,VSI)特性,提出了VSI-DEWMA-RZ控制图;其次,采用蒙特卡罗(Monte-Carlo,MC)仿真模拟所提出控制图的运行链长分布特征,并详细分析了控制图的性能;再次,针对不同的控制图参数,比较了VSI-DEWMA-RZ控制图与DEWMA-RZ和VSI-EWMA-RZ控制图的性能。仿真结果表明,本文提出的VSI-DEWMA-RZ控制图优于DEWMA-RZ控制图,且其对过程中较小和中等偏移的监控效果优于现有的VSI-EWMA-RZ控制图。最后,通过监控食品加工过程中“南瓜籽”和“亚麻籽”的重量,进一步说明了所提出控制图的优越性。
基金funding by King Mongkut’s University of Technology North Bangkok Contract no.KMUTNB-61-KNOW-014
文摘Objective:To define the alert levels for the total number of COVID-19 cases derived by using quantile functions to monitor COVID-19 outbreaks via an exponentially weighted moving-average(EWMA)control chart based on the first hitting time of the total number of COVID-19 cases following a symmetric logistic growth curve.Methods:The cumulative distribution function of the time for the total number of COVID-19 cases was used to construct a quantile function for classifying COVID-19 alert levels.The EWMA control chart control limits for monitoring a COVID-19 outbreak were formulated by applying the delta method and the sample mean and variance method.Samples were selected from countries and region including Thailand,Singapore,Vietnam,and Hong Kong to generate the total number of COVID-19 cases from February 15,2020 to December 16,2020,all of which followed symmetric patterns.A comparison of the two methods was made by applying them to a EWMA control chart based on the first hitting time for monitoring the COVID-19 outbreak in the sampled countries and region.Results:The optimal first hitting times for the EWMA control chart for monitoring COVID-19 outbreaks in Thailand,Singapore,Vietnam,and Hong Kong were approximately 280,208,286,and 298 days,respectively.Conclusions:The findings show that the sample mean and variance method can detect the first hitting time better than the delta method.Moreover,the COVID-19 alert levels can be defined into four stages for monitoring COVID-19 situation,which help the authorities to enact policies that monitor,control,and protect the population from a COVID-19 outbreak.
